Symplectic Stafford: the affine same-divisor theorem
Let k be a field of characteristic zero and U a simple, infinite-dimensional k-algebra with an exhaustive nonnegative multiplicative filtration by finite-dimensional k-subspaces. Suppose F_0 U = k and the associated graded algebra is a commutative affine domain of finite Krull dimension. Then for every nonzero d, a in U and every B in U there exist H, R, S in U such that 1 = dR + (B + Ha)dS. The Lean 4 development proves this theorem, its left-handed form, and module generation, stable range and cancellation results for U.
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